Integration points and weights with orthogonal polynomials
This means that the matrix
L_{ik} has an inverse with the properties
\begin{equation*}
\hat{L}^{-1}\hat{L} = \hat{I}.
\end{equation*}
Multiplying both sides of Eq.
(16) with
\sum_{j=0}^{N-1}L_{ji}^{-1} results in
\begin{equation}
\sum_{i=0}^{N-1}(L^{-1})_{ki}Q_{N-1}(x_i)=\alpha_k.
\tag{17}
\end{equation}